非线性叠加原理与Wei-Norman方法
The nonlinear superposition principle and the Wei-Norman method
摘要：
利用群论方法研究了Riccati方程的一些性质，Riccati方程是唯一一个具有非线性叠加原理的微分方程。应用Wei-Norman方法得到了$SL(2,R)$群中的相关微分方程。从群论的角度分析了一阶微分方程组的叠加原理和Lie-Scheffers定理。最后，将该理论应用于非定常薛定谔方程等二阶微分方程的求解
英文摘要：
Group theoretical methods are used to study some properties of the Riccati equation, which is the only differential equation admitting a nonlinear superposition principle. The Wei-Norman method is applied to obtain the associated differential equation in the group $SL(2,R)$. The superposition principle for first order differential equation systems and Lie-Scheffers theorem are also analysed from this group theoretical perspective. Finally, the theory is applied in the solution of second order differential equations like time-independent Schroedinger equation
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
